Chromatic completion

TL;DR

This paper generalizes the chromatic convergence theorem to not necessarily finite spectra and investigates the relationship between the chromatic limit and harmonic localization.

Contribution

It extends the chromatic convergence theorem to broader spectra and clarifies that the chromatic limit does not always match harmonic localization, answering Ravenel's question.

Findings

Chromatic tower limit for non-finite spectra is established.

The chromatic limit generally differs from harmonic localization.

The work generalizes classical chromatic convergence results.

Abstract

We study the limit of the chromatic tower for not necessarily finite spectra, obtaining a generalization of the chromatic convergence theorem of Hopkins and Ravenel. Moreover, we prove that in general this limit does not coincide with harmonic localization, thereby answering a question of Ravenel's.